How do I make my mesh move 1-1 with the bones
The effect of the armature on the mesh is an accumulation of all bones - to make a section of your mesh follow the action of a single bone you do need to ensure the weights for that single bone are all at 1.0, but also you need to ensure that the weights for that section of mesh are zero for all other bones - otherwise the other bones will also be affecting its deformation, negating some of the effect.